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  • Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. y ^ 2 / 9 - x ^ 2 / 27 = 1

2.  Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

      \frac{y^2}{9} - \frac{x^2}{27} = 1

Answers (1)

best_answer

Given a Hyperbola equation,

\frac{y^2}{9} - \frac{x^2}{27} = 1

Can also be written as 

\frac{y^2}{3^2} - \frac{x^2}{(\sqrt{27})^2} = 1

Comparing this equation with the standard equation of the hyperbola:

\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1

We get,

a=3 and b=\sqrt{27}

Now, As we know the relation in a hyperbola,

c^2=a^2+b^2

c=\sqrt{a^2+b^2}

c=\sqrt{3^2+(\sqrt{27})^2}

c=\sqrt{36}

c=6

Here as we can see from the equation that the axis of the hyperbola is Y-axis. So, 

Coordinates of the foci:

(0,c) \:and\:(0,-c)=(0,6)\:and\:(0,-6)

The Coordinates of vertices:

(0,a) \:and\:(0,-a)=(0,3)\:and\:(0,-3)

The Eccentricity:

e=\frac{c}{a}=\frac{6}{3}=2

The Length of the latus rectum :

\frac{2b^2}{a}=\frac{2(27)}{3}=\frac{54}{3}=18

Posted by

Pankaj Sanodiya

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